Crystal chemistry of the magnetite-ulvospinel series

Spinel single crystals of 19 compositions along the magnetite-ulvospinel join were synthesized by use of a flux-growth method. To obtain quantitative site populations, the crystals were analyzed by single-crystal X-ray diffraction, electron-microprobe techniques, and Mossbauer spectroscopy. All results were processed by using an optimization model. The unit-cell parameter, oxygen fractional coordinate, and tetrahedral bond length increase with increasing ulvospinel component, whereas the octahedral bond length decreases marginally. These changes result in sigmoidal crystal-chemical relationships consistent with cation substitutions in fully occupied sites. As a first approximation, the Akimoto model [sup.T] [([Fe.sup.3+.sub.1-X][Fe.sup.2+.sub.X].sup.M][Fe.sup.2+][Fe.sup.3+.sub.1-X] [Ti.sub.X])[O.sub.4] describes the cation substitutions. Deviations from this model can be explained by an electron exchange reaction [sup.T] [Fe.sup.2+] + [sup.M][Fe.sup.3+] = [sup.T][Fe.sup.3+] + [sup.M][Fe.sup.2+], which causes [sup.M][Fe.sup.2+] [not equal to] 1 and [sup.T][Fe.sup.2+]/Ti [not equal to] 1. The resultant S-shaped trends may be related to a directional change in the electron exchange reaction at Ti [approximately equal to] 0.7 apfu. In general, variations in structural parameters over the whole compositional range can be split into two contributions: (1) a linear variation due to the [sup.T][Fe.sup.3+] + [sup.M][Fe.sup.3+] = [sup.T][Fe.sup.2+] + [sup.M][Ti.sup.4+] chemical substitution and (2) non-linear variations caused by the internal electron exchange reaction. In accordance with bond-valence theory, strained bonds ascribable to steric effects characterize the structure of magnetite-ulvospinel crystals. To relax the bonds and thereby minimize the internal strain under retained spinel space group symmetry, the electron exchange reaction occurs. Keywords: Spinel, Mossbauer spectroscopy, crystal synthesis, crystal structure